We study the influence of quantum geometry on the magnetic responses of quadratic band crossing semimetals. More explicitly, we examine the Landau levels, quantum Hall effect, and magnetic susceptibility of a general two-band Hamiltonian that has fixed isotropic quadratic band dispersion but with tunable quantum geometry, in which the interband coupling is fully characterized by the maximum quantum distance dmax. By continuously tuning dmax in the range of 0≤dmax≤1, we investigate how the magnetic properties of the free-electron model with dmax=0 evolve into those of the bilayer graphene with dmax=1. We demonstrate that despite sharing the same energy dispersion ϵ(p)=±p22m, the charge carriers in the free-electron model and bilayer graphene exhibit entirely distinct Landau levels and quantum Hall responses due to the nontrivial quantum geometry of the wave functions.
We thank H. Watanabe, M. Koshino, T. Soejima, and J. Jung for the useful discussions. C-g.O. was supported by Q-STEP, WINGS Program, the University of Tokyo. J.W.R. was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korean government (MSIT) (Grants No. 2021R1A2C1010572, No. 2021R1A5A1032996, and No. 2022M3H3A106307411) and the Ministry of Education (Grant No. RS-2023-00285390). B.-J.Y. was supported by Samsung Science and Technology Foundation under Project No. SSTF-BA2002-06, NRF grants funded by the government of Korea (MSIT) (Grant No. NRF-2021R1A5A1032996), and GRDC (Global Research Development Center) Cooperative Hub Program through the NRF funded by the Ministry of Science and ICT (MSIT) (Grant No. RS-2023-00258359).
